17 Aug Provide a relevant graph of the function and an explanation of how the graph shows discontinuity at c.
A. Define a function, f(x), and pick a value c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal and the function is continuous.
1. Provide a relevant graph of the function and an explanation of how the graph shows continuity.
2. Show the values of the limits and explain why the defined function is continuous according to the definition of continuity.
B. Define a function, f(x), and pick a value c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal, the function is defined at c but the function is not continuous at c.
1. Provide a relevant graph of the function and an explanation of how the graph shows discontinuity at c.
2. Show the values of the limits and explain why the function is not continuous using the definition of continuity.
C. Define a function, f(x), and pick a value c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are equal, the function is not defined at c and the function is not continuous at c.
1. Provide a relevant graph of the function and an explanation of how the graph shows discontinuity at c.
2. Show the values of the limits and explain why the function is not continuous using the definition of continuity
D. Define a function, f(x), and pick a value c such that the limit of f(x) as x approaches c from the right and the limit of f(x) as x approaches c from the left are not equal in value.
1. Provide a relevant graph of the function and an explanation of how the graph shows discontinuity at c.
2. Explain why the limit of f(x) as x approaches c does not exist and why the function is not continuous using the definition of continuity.
